where \(\theta (f)\)  is the sheaf of vector fields along \(f\) , and \(T(f)\)  is the extended \(\) -tangent space of \(f\) , see [1]}. What gives its name to the instability locus is the following result from
[2]}:


Let \(f\colon M\rightarrow N\)  be a \(\) -finite map, let \(q\in N\)  and \(S=f^{-1}(q)\cap \Sigma (f)\) . If \(q\notin \mathrm {Inst}(f)\) , then the germ of \(f\)  at \(S\)  is stable.
